How can I animate an interior scene from day to night?
If you are using Cycles or Eevee

Light your scene with:


a world node setup using a Mix node between two Environment textures: 


a nightlight texture like this
a not too bright daylight texture without a visible sun direction (highly overcast) like this, because you will like to add and animate the Sun yourself

a sun lamp with some "midday" inclination, parented to an Empty that stays at ground level in the middle of the scene (you could also put the sun lamp directly in the middle, but with an Empty it "looks" nicer while you work on it).
indoor lights


Animate by setting these keyframes:


Starting frame: 


the Empty is rotated such that the sun is high in the sky. 
The sun Energy is high. The sun color can be slightly orange if the daylight world texture is slightly blue
The world Mix factor is at 1.0 (completely daylight)
no keyframes for indoor lights

at ~80% of the transition


indoor lights Energy is zero
no keyframes for world/sun

at ~80% of the transition + a few frames 


indoor lights Energy is high
no keyframes for world/sun

Last frame:


The Empty is rotated along either the X or the Y axis in a way such that the sun goes just slightly below (and parallel to) the horizon
The sun Energy is zero. The sun color is neutral.
The world Mix factor is at 0.0
no keyframes for indoor lights